Re: Simplifying Logs

*To*: mathgroup at smc.vnet.net*Subject*: [mg113127] Re: Simplifying Logs*From*: Raffy <adraffy at gmail.com>*Date*: Wed, 13 Oct 2010 23:28:01 -0400 (EDT)*References*: <i93k7o$e4s$1@smc.vnet.net>

On Oct 12, 11:39 pm, Themis Matsoukas <tmatsou... at me.com> wrote: > This works as expected and combines the logs: > > Simplify[Log[a] - Log[b], Assumptions -> {a > 0, b > 0}] > > Log[a/b] > > But this doesn't: > > Simplify[1 + Log[a] - Log[b], Assumptions -> {a > 0, b > 0}] > > 1 + Log[a] - Log[b] > > This seems inconsistent to me. I suppose I would like to see a CombineLog= s command in the future. > > Themis 1 + Log[a/b] // LeafCount === 8 1 + Log[a] - Log[b] // LeafCount === 8 ClearAll[exprSize]; exprSize[x_] := StringLength@ToString[Unevaluated[x], InputForm]; SetAttributes[exprSize,HoldFirst]; Caution: exprSize[1+1] ==> "1 + 1" ==> 5 1 + Log[a/b] // exprSize === 12 1 + Log[a] - Log[b] // exprSize === 19 Simplify[1 + Log[a] - Log[b], Assumptions -> {a > 0, b > 0}, ComplexityFunction -> exprSize] === 1 + Log[a/b] It would be great for Mathematica to support multiple complexity functions in case of a tie, similar to SortBy/GatherBy/SplitBy/etc. ie. ComplexityFunction -> {LeafCount, exprSize}